○ Alexander Shatskiy considered a technique of calculating deflection of the light passing through wormholes (from one universe to another). He found fundamental and characteristic features of electromagnetic radiation passing through the wormholes.
○ He showed that the distortion of the light rays that had passed through the WH throat is caused not only by redistributing of the star density, but also by changes in their apparent brightness.
○ He also implied that if angular resolution of the observer’s instrument in our Universe is high enough, he will be able to discover the changing star density in the throat J(h).
○ He also showed that the apparent brightness of the WH’s part inside its throat does not depend on impact parameter.
Alexander Shatskiy considered a technique of calculating deflection of the light passing through wormholes (from one universe to another). He found fundamental and characteristic features of electromagnetic radiation passing through the wormholes. Making use of this, he proposed new methods of observing distinctive differences between wormholes and other objects as well as methods of determining characteristic parameters for different wormhole models.
By modifying Einstein equations, he first obtained the explicit analytical form of the solution to the first order in the small correction δ ( being defined by the equation-of-state of the matter in the WH) and then transcendental equation yielding the throat radius.
In order to know, what causes the distortion of light in wormhole, he considered that the other universe contain N stars with equal luminosities and supposed N >>> 1.
Then he assumed that, all the stars are homogeneously distributed over the celestial sphere in the other universe. An observer in our Universe who is looking at the stars in the other universe through the WH throat sees them inhomogeneously distributed over the throat. This is because of the fact that the WH throat refracts and distorts the light of these stars. The distortion will obviously be spherically symmetric with the throat center being the symmetry center.
Later, he assumed that the observer look only at the fraction of the stars seen in the thin ring with the center coinciding with the throat center, the ring radius being h and its width – dh. Hence, the observer surveys the solid angle dΩ of the other universe and, moreover, dΩ = 2π|sin θ| dθ. Here, θ(h) is the deflection angle of light rays passing through the WH throat measured relative to the rectilinear propagation (By convention, the rectilinear propagation means the trajectory passing through the center of the WH throat) . Since the total solid angle equals 4π, the observer can see dN = N dΩ/(4π) stars in the ring (Since the light deflection angle θ can exceed π, the total solid angle turns out to be more than 4π. This change, however, reduces to another constant (instead of 4π) and does not affect the final result.). Furthermore, the apparent density of the stars (per unit area of the ring dS = 2πh dh) is J = dN/dS. He, therefore, obtain:
The dependance θ(h),
where, the notations η ≡ 1/x and h˜ ≡ h/q were used. This yields
Taking advantage of all these formulae, they found the expression for the apparent density of the stars J(h) in the wormhole.
He noted that, 2nd formula/equation also gives the maximum possible impact parameter h = hmax which still allows the observer to see the stars of the other universe. This parameter corresponds to a zero of the second factor in the radicand in (2). Namely, hmax is equal to the least possible value of the function e^–φ / η. Having conducted trivial inquiry, he obtained:
What all these equations actually showed that the distortion of the light rays that had passed through the WH throat is caused not only by redistributing of the star density, but also by changes in their apparent brightness. Namely, as the impact parameter h increases the stellar brightness changes. This is because of the fact that as the radius h of the ring, through which the star light passes, increases, an element of the solid angle where this light scatters changes as well. The respective change in the stellar brightness is proportional to the quantity κ = dS/dΩ. Therefore, the total brightness of all the stars seen on unit area of the above-mentioned ring is dN · κ/dS.
Thus, he obtained that as N → ∞ the apparent brightness of the WH’s part inside its throat does not depend on impact parameter and, regardless of which WH model he used, the WH looks like a homogeneous spot in every wavelength range.
In spite the result obtained stating that the light distribution in the WH throat is homogeneous for each WH model, he also noted that in the real universe the number of visible stars is finite, though big. This implies that if angular resolution of the observer’s instrument in our Universe is high enough, he will be able to discover the changing star density in the throat J(h).
The left panel of Fig. 1 shows this plot for δ = 0.001. Sharp minima on the plot correspond to zeros of the sine in equation 1. This is because at sufficiently large impact parameters the light rays are deflected by large angles (θ > π) so that in the vicinities of the points θ = πn abrupt declines in distribution arise. But near these declines the observed stellar brightness tends to infinity (lensing), which ultimately provides the (on average) uniform light flow over the WH throat (see the right panel of Fig. 1).
Positions of the declines depend on the value of δ. Hence, registering them makes it possible to determine the equation-of-state parameters of the WH matter and features of the WH model (which is highly analogous to processing the light spectra).
Reference: Alexander Shatskiy, “Image of another universe being observed through a wormhole throat”, Astronomical Journal, pp. 1-6, 2012. https://arxiv.org/abs/0809.0362
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